Data in B-meson decays indicate violations of lepton flavour universality, thereby raising the question about such phenomena in the charm sector. We perform a model-independent analysis of NP contributions in (semi)-leptonic decays of $$D_{(s)}$$ $D_{\left(s\right)}$ mesons which originate from $$c \rightarrow d \bar{{\ell }} \nu _l$$ $c\to d\overline{\ell }{\nu }_l$ and $$c \rightarrow s \bar{{\ell }} \nu _{\ell }$$ $c\to s\overline{\ell }{\nu }_{\ell }$ charged-current interactions. Starting from the most general low-energy effective Hamiltonian containing four-fermion operators and the corresponding short-distance coefficients, we explore the impact of new (pseudo)-scalar, vector and tensor operators and constrain their effects through the interplay with current data. We pay special attention to the elements $$|V_{cd}|$$ $|V_{\mathrm{cd}}|$ and $$|V_{cs}|$$ $|V_{\mathrm{cs}}|$ of the Cabibbo–Kobayashi–Maskawa matrix and extract them from the $$D_{(s)}$$ $D_{\left(s\right)}$ decays in the presence of possible NP decay contributions, comparing them with determinations utilizing unitarity. We find a picture in agreement with the Standard Model within the current uncertainties. Using the results from our analysis, we make also predictions for leptonic $$D_{(s)}^+ \rightarrow e^+ \nu _e$$ $D_{\left(s\right)}^{+}\to e^{+}{\nu }_e$ modes which could be hugely enhanced with respect to their tiny Standard Model branching ratios. It will be interesting to apply our strategy at the future high-precision frontier.